Related papers: Data-Driven Snapshot Calibration via Monotonic Fea…

Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…

The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Current few-shot learning models capture visual object relations in the so-called meta-learning setting under a fixed-resolution input. However, such models have a limited generalization ability under the scale and location mismatch between…

Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and…

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

The accurate determination of atom numbers is an ubiquitous problem in the field of ultracold atoms. For modest atom numbers, absolute calibration techniques are available, however, for large numbers and high densities, the available…

Dominant features of spatial data are connected structures or patterns that emerge from location-based variation and manifest at specific scales or resolutions. To identify dominant features, we propose a sequential application of…

While raw cosine similarity in pretrained embedding spaces exhibits strong rank correlation with human judgments, anisotropy induces systematic miscalibration of absolute values: scores concentrate in a narrow high-similarity band…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

Freezing the pre-trained backbone has become a standard paradigm to avoid overfitting in few-shot segmentation. In this paper, we rethink the paradigm and explore a new regime: {\em fine-tuning a small part of parameters in the backbone}.…

Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…

Enhancing forward-looking sonar images is critical for accurate underwater target detection. Current deep learning methods mainly rely on supervised training with simulated data, but the difficulty in obtaining high-quality real-world…

Functions with jumps and kinks typically arising from parameter dependent or stochastic hyperbolic PDEs are notoriously difficult to approximate. If the jump location in physical space is parameter dependent or random, standard…

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…

Multi-frame methods improve monocular depth estimation over single-frame approaches by aggregating spatial-temporal information via feature matching. However, the spatial-temporal feature leads to accuracy degradation in dynamic scenes. To…

We present a solution to the problem of spatio-temporal calibration for event cameras mounted on an onmi-directional vehicle. Different from traditional methods that typically determine the camera's pose with respect to the vehicle's body…

We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…

Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…